Modal and temporal logics for processes

Stirling, Colin

doi:10.1007/3-540-60915-6_5

Cited by 149 publications

(184 citation statements)

References 52 publications

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“…We consider two common notions of abstraction: simulation [Mil71], which preserves only universal properties, and bisimulation [Par81], which preserves properties of the full mu-calculus (cf. [BCG88,Sti95]). Let M and N be LTS's, with…”

Section: Lifting Proofsmentioning

confidence: 99%

“…We assume that R is total : i.e., for any s and a, there exists t such that (s, a, t) ∈ R. A set, I, of initial states can be accommodated by adding a dummy initial state with a transition to each state in I. The evaluation of a formula f , represented as f c , is a subset of S, defined relative to a context c mapping variables to subsets of S. The evaluation rules are standard (see, e.g., [Sti95]) and are omitted here. A state s in the LTS satisfies a closed mu-calculus formula f iff s ∈ f ⊥ , where ⊥ maps every variable to the empty set.…”

Section: Introductionmentioning

confidence: 99%

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Lifting Temporal Proofs through Abstractions

Namjoshi¹

2002

Lecture Notes in Computer Science

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Abstract. Model checking is often performed by checking a transformed property on a suitable finite-state abstraction of the source program. Examples include abstractions resulting from symmetry reduction, data independence, and predicate abstraction. The two programs are linked by a structural relationship, such as simulation or bisimulation, guaranteeing that if the transformed property holds on the abstract program, the property holds on the original program. Recently, several algorithms have been developed to automatically generate a deductive proof of correctness from a model checker. A natural question, therefore, is how to 'lift' a deductive proof that is generated for an abstract program back into the original program domain. In this paper, we show how this can be done for general temporal properties, relative to several types of abstraction relationships between the two programs. We develop simplifications of the lifting scheme for common types of abstractions, such as predicate abstraction. We also show how one may generate easily checkable lifted proofs, which find use in applications such as proof-carrying code, and in the use of model checkers as decision procedures in theorem proving.

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Section: Lifting Proofsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lifting Temporal Proofs through Abstractions

Namjoshi¹

2002

Lecture Notes in Computer Science

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“…The similarity between the interpretative structures in object-oriented models and labeled transition systems reflects in a similarity between object-oriented models and modal logics of programs, which are formalisms specifically designed for reasoning about program schemes, and which are interpreted in terms of labeled transition systems (see [20,23] for surveys).…”

Section: Reasoning In Cvlmentioning

confidence: 99%

Structured objects: Modeling and reasoning

Calvanese

Giacomo

Lenzerini

1995

Deductive and Object-Oriented Databases

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Abstract. One distinctive characteristic of object-oriented data models over traditional database systems is that they provide more expressive power in schema definition. Nevertheless, the defining power of objectoriented models is still somewhat limited, mainly because it is commonly accepted that part of the semantics of the application can be represented within methods. The research work reported in this paper explores the possibility of enhancing the power of object-oriented data models in schema definition, thus offering more possibilities to reason about the intension of the database and better supporting data management. We demonstrate our approach by presenting a new data model, called CVL, that extends the usual object-oriented data models with several aspects, including view definition, recursive structure modeling, navigation of the schema through forward and backward traversal of links (attributes and relations), subsetting of attributes, and cardinality ratio constraints on links. CVL is equipped with sound, complete, and terminating inference procedures, that allow various forms of reasoning to be carried out on the intensional level of the database. IntroductionOne distinctive characteristic of object-oriented data models over traditional database systems is that they provide more expressive power in schema definition. Indeed, several modeling constructs of object-oriented data models are borrowed from the research on semantic data modeling and semantic networks in Artificial Intelligence, and are intended to overcome well-known limitations of flat data representation. Nevertheless, the defining power of object-oriented models is still somewhat limited. Examples of useful representation mechanisms that are considered important especially for new applications, but are generally not considered in object-oriented schemas are: recursive class definitions, view definitions, cardinality ratio constraints on attributes, subsetting of attributes, inverse of attributes, union and complement of classes (see for example [9]). One reason for limiting the expressivity of schemas is that object-oriented models support method definitions, and it is generally accepted that some of the semantics of the application could be very well represented within methods.The research work reported in this paper explores the possibility of enhancing the power of object-oriented data models in schema definition. We argue that such enhancement is interesting from different points of view:-Capturing more semantics at the schema level allows the designer to declaratively represent relevant knowledge about the classes of the application. It follows that sophisticated types of constraints can be asserted in the schema, rather than embedding them in methods, with the advantage of devising general integrity checking methods to be included in future database systems. -Expressing more knowledge at the schema level implies more possibilities to reason about the intension of the database. Such reasoning can be exploited for deriving usefu...

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“…Most of them, if not all, base their definitions on the (bi)simulation game that characterizes (bi)simulations between processes [11,3,2]. Although these are branching semantics, their co-inductive characterizations provide a (partially) local way to compare processes by considering, one by one, all the possible transitions from the compared states.…”

Section: Introductionmentioning

confidence: 99%

Defining Distances for All Process Semantics

Hernández

Frutos-Escrig

2012

Formal Techniques for Distributed Systems

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Abstract. Recently several authors have proposed some notions of distance between processes that try to quantify "how far away" is a process to be related with some other with respect to a certain semantics. These proposals are usually based on the simulation game, and therefore are mainly defined for simulation semantics or other semantics more or less close to these. These distances have a local character since only one of the successors of each state is taken into account in their computation. Here, we present an alternative proposal exploiting the fact that processes are trees. We define the distance between two of them as the cost of the transformations that we need to apply to get two processes related by the corresponding semantics. Our new distances can be uniformly defined for all the semantics in the ltbt-spectrum.

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Modal and temporal logics for processes

Cited by 149 publications

References 52 publications

Lifting Temporal Proofs through Abstractions

Lifting Temporal Proofs through Abstractions

Structured objects: Modeling and reasoning

Defining Distances for All Process Semantics

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